In English. Summaries in Estonian

Proceedings of the Estonian Academy of Sciences.

Physics * Mathematics


Volume 50 No. 3 September 2001


Semiparallel submanifolds with plane generators of codimension two in a Euclidean space; 115–123

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Abstract. A submanifold generated by plane leaves of codimension two in a Euclidean space is, in general, intrinsically a Riemannian manifold of conullity two. All such manifolds have been classified into four classes: planar, hyperbolic, parabolic, and elliptic, i.e. having, respectively, infinitely many, two, one, or no real intrinsically asymptotic distributions. It is proved that if such a submanifold is semiparallel and intrinsically a manifold of conullity two, then it must be planar. This verifies, for the case considered here, a conjecture that a semiparallel submanifold, which is intrinsically of conullity two, must be planar. Validity of this conjecture has been established previously by the author for the three-dimensional semiparallel submanifolds.

Key words: Riemannian manifolds of conullity two, asymptotic foliations, semiparallel submanifolds.

Pseudosymmetric contact metric manifolds in the sense of M. C. Chaki; 124–132

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Kadri ARSLAN, Cengizhan MURATHAN, Cihan ÖZGÜR, and


Abstract. We consider pseudosymmetric and pseudo Ricci symmetric manifolds in the sense of M. C. Chaki. The case  is assumed to be a contact metric manifold with  belonging to -nullity distribution.

Key words: contact manifolds, Einstein -Einstein) manifolds, -nullity distribution, pseudosymmetric manifolds of Chaki type.

Fully discrete collocation method for weakly singular integral equations; 133–144

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Abstract. To find the approximate solutions of a weakly singular integral equation by the collocation method it is necessary to solve linear systems whose coefficients are expressed as integrals. These integrals cannot usually be computed exactly. We get the fully discrete collocation method when we approximate the integrals by quadrature formulas on nonuniform grid. In this paper an appropriate grid is formed and the dependence of the convergence rate of this method on the choice of the grid is studied.

Key words: weakly singular integral equation, collocation method.

Fast solvers of generalized airfoil equation of index –1; 145–154

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Abstract. We consider the generalized airfoil equation in the situation where the index of the problem is –1. We periodize the problem, then discretize it by a fully discrete version of the trigonometric collocation method and apply the conjugate gradient method to solve the discretized problem. The approximate solution appears to be of optimal accuracy in a scale of Sobolev norms, and the N parameters of the approximate solution can be determined by O(N log N) arithmetical operations.

Key words: airfoil equations, fast solvers.

Application of wavelet transform techniques to vibration studies; 155–168

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Abstract. Wavelet transform techniques are applied to analysis of linear vibrations. It is shown that in some simple cases wavelet transform can be accomplished analytically. Damped and forced vibrations of single and two degrees of freedom are considered. The achieved results can be used for interpreting more complicated cases.

Key words: linear vibrations, damped and forced vibrations, Fourier transform, wavelets.

Properties of high-temperature superconductors in a two-band model with the doping-dependent electron spectrum; 169–178

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Nikolai KRISTOFFEL and Pavel RUBIN

Abstract. A simple model of interband superconductivity, incorporating a basic band and a doping created one (constant total number of states), is considered, keeping in mind the two-component scenario of high-Tc superconductivity. The dependences of Tc, its isotope exponent, superconductivity gaps, etc. on doping are calculated using an illustrative set of parameters. The observed types of behaviour are reproduced. Diminishing gap ratios with hole doping have been found. In the one-particle excitation spectrum the peak–dip–hump type complex can be identified. In spite of crude approximations the model reflects, in general, the experimental findings on high-Tc cuprates. Two-band models will remain a channel for looking for the high-Tc mechanism.

Key words: high-temperature superconductivity, two-band models, doping, gaps.



Ülo Lepik 80; 179